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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis).

Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proof.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements.

Mathematics is essential in many fields, including natural science, engineering, medicine, finance, and the social sciences.

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